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GCOE lecture series
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
2012/11/28
14:50-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Haim Brezis (Rutgers University / Technion)
Can you hear the degree of a map from the circle into itself? An intriguing story which is not yet finished (ENGLISH)
Haim Brezis (Rutgers University / Technion)
Can you hear the degree of a map from the circle into itself? An intriguing story which is not yet finished (ENGLISH)
[ Abstract ]
A few years ago - following a suggestion by I. M. Gelfand - I discovered an intriguing connection between the topological degree of a map from the circle into itself and its Fourier coefficients. This relation is easily justified when the map is smooth. However, the situation turns out to be much more delicate if one assumes only continuity, or even Holder continuity. I will present recent developments and open problems. The initial motivation for this direction of research came from the analysis of the Ginzburg-Landau model.
A few years ago - following a suggestion by I. M. Gelfand - I discovered an intriguing connection between the topological degree of a map from the circle into itself and its Fourier coefficients. This relation is easily justified when the map is smooth. However, the situation turns out to be much more delicate if one assumes only continuity, or even Holder continuity. I will present recent developments and open problems. The initial motivation for this direction of research came from the analysis of the Ginzburg-Landau model.
